https://doi.org/10.1140/epjp/s13360-021-01813-1
Regular Article
Application of the Lie symmetry approach to an extended Jimbo–Miwa equation in (3+1) dimensions
1
Department of Mathematics, Faculty of Mathematical Sciences, University of Delhi, 110007, New Delhi, Delhi, India
2
Department of Mathematics, Zhejiang Normal University, 321004, Jinhua, Zhejiang, China
3
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia
4
Department of Mathematics and Statistics, University of South Florida, 33620-5700, Tampa, FL, USA
5
School of Mathematical and Statistical Sciences, North-West University, Private Bag X2046, Mafikeng Campus, 2735, Mmabatho, South Africa
Received:
4
January
2021
Accepted:
29
July
2021
Published online:
15
August
2021
In this article, we study Lie point symmetries, closed-form invariant solutions, and dynamics of exact solitons to an extended (3+1)-dimensional Jimbo–Miwa (JM) equation by employing the Lie symmetry method. Under the resulting symmetries, the extended JM equation is reduced to lower-dimensional equations. We exploit the travelling wave ansatz to determine closed-form invariant solutions of the reduced equations. The physical interpretations of the obtained solutions are exhibited in the forms of single solitons, multi-wave solitons, multiple solitons with parabolic waves, oscillating lump solitons, triply solitons, and double solitons via numerical simulation for adequate choices of the involved arbitrary constants through the mathematical software Wolfram Mathematica. These constructed solutions can help us better understand interesting nonlinear complex phenomena and mechanisms.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021